Hi all.
I believe that this question was asked here before however I still cant find a solution.

Laets say I have got 2 layers. Layer 1 is a square blue color and layer 2 is a green circle. Green circle is positioned so half of circle is outside that squer and half inside.
How do I cut off outside half and keep everything in each layer and color as it was?

Tried all different sorts of but nothing seems to work as should.
Thanks.

Put the square above the circle. Select both. Path menu > Intersection

To expand on Brynn's answer, when you use Boolean operations like intersection, it converts two paths into one. So if you still want the blue square left at the end, you'll need to make a copy of it to use for the intersection. Try this approach:

1) Select the blue square.
2) Press CTRL-C to copy it to the clipboard.
3) Select the green circle. This will switch the currently active layer.
4) Press CTRL-ALT-V to "paste in place", putting the copied square in exactly the right position, but in the same layer as the green circle.
5) Select both the green circle and the new blue square. The square should already be selected from step (4), so just hold SHIFT and click on the circle.
6) Path > Intersection (or CTRL-* - if you have a full size keyboard then the * on the numeric keypad is the best option).